{"id":"https://openalex.org/W7131656998","doi":"https://doi.org/10.1007/s10846-026-02366-0","title":"An Optimal Integral Sliding Mode Control Based Time Delay Estimation for Nonlinear Lower Limb Exoskeleton Robot","display_name":"An Optimal Integral Sliding Mode Control Based Time Delay Estimation for Nonlinear Lower Limb Exoskeleton Robot","publication_year":2026,"publication_date":"2026-02-26","ids":{"openalex":"https://openalex.org/W7131656998","doi":"https://doi.org/10.1007/s10846-026-02366-0"},"language":"en","primary_location":{"id":"doi:10.1007/s10846-026-02366-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10846-026-02366-0","pdf_url":null,"source":{"id":"https://openalex.org/S91329792","display_name":"Journal of Intelligent & Robotic Systems","issn_l":"0921-0296","issn":["0921-0296","1573-0409"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Intelligent &amp; Robotic Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1007/s10846-026-02366-0","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5046035634","display_name":"Alrawda Alsaied","orcid":null},"institutions":[{"id":"https://openalex.org/I34949971","display_name":"University of Jinan","ror":"https://ror.org/02mjz6f26","country_code":"CN","type":"education","lineage":["https://openalex.org/I34949971"]},{"id":"https://openalex.org/I4210163399","display_name":"Shandong First Medical University","ror":"https://ror.org/05jb9pq57","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210163399"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Alrawda Alsaied","raw_affiliation_strings":["Institute of Intelligent Medical Engineering, School of Control Science and Engineering, Shandong University, Jinan, Shandong, China"],"affiliations":[{"raw_affiliation_string":"Institute of Intelligent Medical Engineering, School of Control Science and Engineering, Shandong University, Jinan, Shandong, China","institution_ids":["https://openalex.org/I4210163399","https://openalex.org/I34949971"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5121316066","display_name":"K. Li","orcid":null},"institutions":[{"id":"https://openalex.org/I34949971","display_name":"University of Jinan","ror":"https://ror.org/02mjz6f26","country_code":"CN","type":"education","lineage":["https://openalex.org/I34949971"]},{"id":"https://openalex.org/I4210163399","display_name":"Shandong First Medical University","ror":"https://ror.org/05jb9pq57","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210163399"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Ke Li","raw_affiliation_strings":["Institute of Intelligent Medical Engineering, School of Control Science and Engineering, Shandong University, Jinan, Shandong, China"],"affiliations":[{"raw_affiliation_string":"Institute of Intelligent Medical Engineering, School of Control Science and Engineering, Shandong University, Jinan, Shandong, China","institution_ids":["https://openalex.org/I4210163399","https://openalex.org/I34949971"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5108047889","display_name":"Y\u00ec W\u00e1ng","orcid":"https://orcid.org/0000-0001-5697-0717"},"institutions":[{"id":"https://openalex.org/I34949971","display_name":"University of Jinan","ror":"https://ror.org/02mjz6f26","country_code":"CN","type":"education","lineage":["https://openalex.org/I34949971"]},{"id":"https://openalex.org/I4210163399","display_name":"Shandong First Medical University","ror":"https://ror.org/05jb9pq57","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210163399"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jiashuai Wang","raw_affiliation_strings":["Institute of Intelligent Medical Engineering, School of Control Science and Engineering, Shandong University, Jinan, Shandong, China"],"affiliations":[{"raw_affiliation_string":"Institute of Intelligent Medical Engineering, School of Control Science and Engineering, Shandong University, Jinan, Shandong, China","institution_ids":["https://openalex.org/I4210163399","https://openalex.org/I34949971"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5125496085","display_name":"Ghazally I. Y. Mustafa","orcid":null},"institutions":[{"id":"https://openalex.org/I83776822","display_name":"Shandong Institute of Business and Technology","ror":"https://ror.org/03rrkrc24","country_code":"CN","type":"education","lineage":["https://openalex.org/I83776822"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ghazally I. Y. Mustafa","raw_affiliation_strings":["School of Information and Electronic Engineering, Shandong Technology and Business University, Yantai, Shandong, China"],"affiliations":[{"raw_affiliation_string":"School of Information and Electronic Engineering, Shandong Technology and Business University, Yantai, Shandong, China","institution_ids":["https://openalex.org/I83776822"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5121316066"],"corresponding_institution_ids":["https://openalex.org/I34949971","https://openalex.org/I4210163399"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.58769551,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"112","issue":"2","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11023","display_name":"Prosthetics and Rehabilitation Robotics","score":0.8203999996185303,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11023","display_name":"Prosthetics and Rehabilitation Robotics","score":0.8203999996185303,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10510","display_name":"Stroke Rehabilitation and Recovery","score":0.05040000006556511,"subfield":{"id":"https://openalex.org/subfields/2742","display_name":"Rehabilitation"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},{"id":"https://openalex.org/T11687","display_name":"Teleoperation and Haptic Systems","score":0.04430000111460686,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.7759000062942505},{"id":"https://openalex.org/keywords/trajectory","display_name":"Trajectory","score":0.6601999998092651},{"id":"https://openalex.org/keywords/particle-swarm-optimization","display_name":"Particle swarm optimization","score":0.5975000262260437},{"id":"https://openalex.org/keywords/exoskeleton","display_name":"Exoskeleton","score":0.5946000218391418},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5103999972343445},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5080999732017517},{"id":"https://openalex.org/keywords/robot","display_name":"Robot","score":0.5037999749183655},{"id":"https://openalex.org/keywords/tracking","display_name":"Tracking (education)","score":0.4733999967575073}],"concepts":[{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.7759000062942505},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.6601999998092651},{"id":"https://openalex.org/C85617194","wikidata":"https://www.wikidata.org/wiki/Q2072794","display_name":"Particle swarm optimization","level":2,"score":0.5975000262260437},{"id":"https://openalex.org/C146549078","wikidata":"https://www.wikidata.org/wiki/Q191944","display_name":"Exoskeleton","level":2,"score":0.5946000218391418},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5902000069618225},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5103999972343445},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5080999732017517},{"id":"https://openalex.org/C90509273","wikidata":"https://www.wikidata.org/wiki/Q11012","display_name":"Robot","level":2,"score":0.5037999749183655},{"id":"https://openalex.org/C2775936607","wikidata":"https://www.wikidata.org/wiki/Q466845","display_name":"Tracking (education)","level":2,"score":0.4733999967575073},{"id":"https://openalex.org/C2778132902","wikidata":"https://www.wikidata.org/wiki/Q6042725","display_name":"Integral sliding mode","level":4,"score":0.45840001106262207},{"id":"https://openalex.org/C36662352","wikidata":"https://www.wikidata.org/wiki/Q6008560","display_name":"Sliding mode control","level":3,"score":0.42010000348091125},{"id":"https://openalex.org/C2776829284","wikidata":"https://www.wikidata.org/wiki/Q1341651","display_name":"Lyapunov stability","level":3,"score":0.40400001406669617},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.39809998869895935},{"id":"https://openalex.org/C48677424","wikidata":"https://www.wikidata.org/wiki/Q6888088","display_name":"Mode (computer interface)","level":2,"score":0.30730000138282776},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.3012999892234802},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.2858999967575073},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.2831000089645386},{"id":"https://openalex.org/C181335050","wikidata":"https://www.wikidata.org/wiki/Q14915018","display_name":"Swarm behaviour","level":2,"score":0.26809999346733093},{"id":"https://openalex.org/C19966478","wikidata":"https://www.wikidata.org/wiki/Q4810574","display_name":"Mobile robot","level":3,"score":0.2669000029563904},{"id":"https://openalex.org/C133731056","wikidata":"https://www.wikidata.org/wiki/Q4917288","display_name":"Control engineering","level":1,"score":0.26589998602867126}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10846-026-02366-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10846-026-02366-0","pdf_url":null,"source":{"id":"https://openalex.org/S91329792","display_name":"Journal of Intelligent & Robotic Systems","issn_l":"0921-0296","issn":["0921-0296","1573-0409"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Intelligent &amp; Robotic Systems","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s10846-026-02366-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10846-026-02366-0","pdf_url":null,"source":{"id":"https://openalex.org/S91329792","display_name":"Journal of Intelligent & Robotic Systems","issn_l":"0921-0296","issn":["0921-0296","1573-0409"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Intelligent &amp; Robotic Systems","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":42,"referenced_works":["https://openalex.org/W1500476116","https://openalex.org/W1955880755","https://openalex.org/W2008788675","https://openalex.org/W2018918594","https://openalex.org/W2104752886","https://openalex.org/W2111509327","https://openalex.org/W2158121031","https://openalex.org/W2395392600","https://openalex.org/W2574540508","https://openalex.org/W2592849791","https://openalex.org/W2621378497","https://openalex.org/W2685803096","https://openalex.org/W2733817478","https://openalex.org/W2737736050","https://openalex.org/W2782847035","https://openalex.org/W2906172613","https://openalex.org/W3007737076","https://openalex.org/W3090682873","https://openalex.org/W3170227478","https://openalex.org/W3173956977","https://openalex.org/W3175159261","https://openalex.org/W4200155585","https://openalex.org/W4211047235","https://openalex.org/W4213053250","https://openalex.org/W4225592410","https://openalex.org/W4225839846","https://openalex.org/W4367838790","https://openalex.org/W4377293823","https://openalex.org/W4385493623","https://openalex.org/W4388529591","https://openalex.org/W4390636023","https://openalex.org/W4392645210","https://openalex.org/W4392797122","https://openalex.org/W4393241722","https://openalex.org/W4400910269","https://openalex.org/W4402616339","https://openalex.org/W4405303522","https://openalex.org/W4408609584","https://openalex.org/W4410975776","https://openalex.org/W4411034570","https://openalex.org/W4412191004","https://openalex.org/W4413472020"],"related_works":[],"abstract_inverted_index":{"Lower-limb":[0],"exoskeleton":[1],"(LLEX)":[2],"robots":[3,19],"are":[4],"becoming":[5],"increasingly":[6],"popular":[7],"for":[8],"aiding":[9],"individuals":[10],"with":[11,40,56,99],"disabilities.":[12],"However,":[13],"the":[14,49,81,89],"tracking":[15,51,130],"performance":[16],"of":[17,53,80],"LLEX":[18,54,102,109],"is":[20,69,85],"significantly":[21],"affected":[22],"by":[23],"system":[24],"uncertainties":[25,114],"and":[26,104,119,134,141],"disturbances.":[27,121],"This":[28],"study":[29],"introduces":[30],"robust,":[31],"optimal":[32,74],"integral":[33],"sliding":[34,75],"mode":[35],"control":[36,136],"(SMC)":[37],"in":[38],"combination":[39],"model-free":[41],"technique-based":[42],"time":[43],"delay":[44],"estimation":[45],"(TDE)":[46],"to":[47,71],"improve":[48],"trajectory":[50,129],"accuracy":[52],"robot":[55],"uncertainties.":[57],"Moreover,":[58],"an":[59,73],"optimization":[60,66],"algorithm":[61,67],"known":[62],"as":[63,116],"particle":[64],"swarm":[65],"(PSO)":[68],"applied":[70],"obtain":[72],"surface":[76],"parameter.":[77],"The":[78,122],"stability":[79],"proposed":[82],"method":[83],"(PSOSMC-TDE)":[84],"theoretically":[86],"approved":[87],"using":[88],"Lyapunov":[90],"function.":[91],"To":[92],"further":[93],"validate":[94],"its":[95],"effectiveness,":[96],"both":[97],"simulations":[98],"a":[100,107],"3D":[101],"model":[103],"experiments":[105],"on":[106],"physical":[108],"platform":[110],"were":[111],"conducted,":[112],"considering":[113],"such":[115],"noise,":[117],"friction,":[118],"external":[120],"results":[123],"demonstrate":[124],"that":[125],"PSOSMC-TDE":[126],"achieves":[127],"precise":[128],"while":[131],"maintaining":[132],"robust":[133],"stable":[135],"signals,":[137],"outperforming":[138],"conventional":[139],"SMC-TDE":[140,145],"nonsingular":[142],"fast":[143],"terminal":[144],"methods.":[146]},"counts_by_year":[],"updated_date":"2026-03-25T13:04:00.132906","created_date":"2026-02-27T00:00:00"}
